Last week's monthly jobs report, showing the economy producing 288,000 jobs in June and the unemployment rate falling to 6.1%, provided the kind of news that White House officials have craved for a long time.

But did the turn come too late to help Democrats in this fall's elections?

Not surprisingly, two schools of thought exist on that question, one espoused mostly by Democratic strategists, the other by Republicans. Neither can offer definitive proof, but for those who hang on each turn in the political news, here are the competing ideas:

First, of course, comes a big caveat: The June report contained a lot of good economic news, and it came after several months of encouraging numbers. But the U.S. economy has seen previous bursts of improvement in the last few years, only to fall back into sluggishness. For the economic news to have a political impact, the current improvement would have to be sustained.

Assuming that happens, the main question is how voters respond to economic news.

Even a small response could matter. The main stake in this fall's elections is control of the Senate. Which party wins could be determined by a few races, in very closely fought states, that could turn on a relative handful of votes.

Many Republican strategists see voters' perceptions of the economy as pretty well locked in at negative. Changing those perpections would require something huge and dramatic, this argument goes, and a slowly improving jobs picture doesn't meet that test.

Along with that argument comes a piece of long-standing political wisdom: that voter perceptions of the economy lag behind the news so much that nothing really matters after late spring.

The counter-argument is that the flow of information, and how people react to it, has sped up so much in recent years that economic data from the summer or even the early fall can have a significant impact. Some Democratic strategists have seized on that idea to justify optimism.

The truth is that neither side really knows who's right. Underneath the confident assertions both sides make -- and some commentators repeat -- lies considerable doubt.

If an improving economy does begin to pay political benefits for Democrats, the impact might not show up in President Obama's approval ratings, which have spent most of this year in the mid-to-low 40s. Recently, problems in Iraq and elsewhere have seemed to weigh down Obama's ratings.

A different gauge to keep an eye on would be a question used by many pollsters, which asks Americans whether they believe the country is generally headed in the "right direction" or is on the "wrong track."

In 2012, the "right direction" number rose fairly steadily, which forecast good news for the incumbent seeking reelection. But that number tumbled during 2013 and has remained mired at a low level ever since.

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